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Simplifying 2x2 + 11x + 13 = 0 Reorder the terms: 13 + 11x + 2x2 = 0 Solving 13 + 11x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 5.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 5.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 5.5x + x2 = 0 + -6.5 5.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 5.5x + x2 = -6.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -6.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -6.5 + 7.5625 Combine like terms: -6.5 + 7.5625 = 1.0625 7.5625 + 5.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 2.75) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 2.75 = 1.030776406 Simplifying x + 2.75 = 1.030776406 Reorder the terms: 2.75 + x = 1.030776406 Solving 2.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 1.030776406 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 1.030776406 + -2.75 x = 1.030776406 + -2.75 Combine like terms: 1.030776406 + -2.75 = -1.719223594 x = -1.719223594 Simplifying x = -1.719223594Subproblem 2
x + 2.75 = -1.030776406 Simplifying x + 2.75 = -1.030776406 Reorder the terms: 2.75 + x = -1.030776406 Solving 2.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -1.030776406 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -1.030776406 + -2.75 x = -1.030776406 + -2.75 Combine like terms: -1.030776406 + -2.75 = -3.780776406 x = -3.780776406 Simplifying x = -3.780776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.719223594, -3.780776406}
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